Answer:
[tex]-9\sqrt{11}[/tex]; None of the above; [tex]3\sqrt{7}[/tex]
Step-by-step explanation:
For the first question:
[tex]5\sqrt{11}-12\sqrt{11}-2\sqrt{11}[/tex]
Treating the radicals as a variable, we combine like terms:
[tex]5\sqrt{11}-12\sqrt{11}-2\sqrt{11}\\\\=-7\sqrt{11}-2\sqrt{11}\\\\-9\sqrt{11}[/tex]
For the second question:
[tex]5(10-4\sqrt{2})[/tex]
We use the distributive property:
[tex]5(10-4\sqrt{2})\\\\5\times 10-5\times4\sqrt{2}\\\\50-20\sqrt{2}[/tex]
This is not one of the choices available.
For the third question:
[tex]\sqrt{3}\times \sqrt{21}[/tex]
We will first find the prime factorization of 21. 21 = 3*7:
[tex]\sqrt{3}\times \sqrt{3\times7}[/tex]
These can all be written under one radical:
[tex]\sqrt{3\times 3\times 7}[/tex]
For square roots, we want pairs of factors. We have a pair of 3s, so this comes out, giving us
[tex]3\sqrt{7}[/tex]
Answer: Answer of First Question is -9√11, answer of second Question is 'None of the above' and answer of third question is 3√7
Step-by-step explanation:
since, in first question, given expression is,
5√11-12√11-2√11
And, we can write, 5√11-12√11-2√11=-9√11
In other words, negative 9 square root of 11
Thus, option third is correct.
In second question, given expression is,
5(10-4√2),
And we can write, 5(10-4√2)=50-20√2
In other words, 50 minus 20 square root of 2.
Thus, Option fourth is correct.
In third question, given expression,
√3×√21,
And we can write, √3×√21=√3×√3×√7=3√7
Thus, third option is correct.
